Functions and graphs: definition of functions, composition of numbers, inverse functions and their graphical representations.

Linear Equations: definitions of lines in the plane, their equations and graphical representation, gradients, normals, intersection of lines and shortest distance from a point to a line.

Quadratic equations: their definition, their graphs, factorisation, completing the square(vertex form), solving the quadratic equation, finding the maximum and minimum of quadratics, intersection of quadratic equations with lines and other quadratics, quadratics in other guises, polynomials, roots, odd/even functions and circles.

Limits: Definition of a limit of a sequence, the number e, algebra of limits for sequences, limits of functions, algebra of limits for functions, continuity, one sided limits and intermediate limits.

Exponentials and logarithms: Their definitions, their graphs, their derivatives, their MacLaurin series, and general exponentials and logarithms.

Complex numbers: Definition of i, a complex number, the argand diagram, the complex plane, polar representation of a complex number, argument of a complex number, Eulers formula (exponential representation of a complex number) and De Movoire’s theorem.

The total mark for the course will be 10% coursework and 90% unseen exam at the end of the year.